Analyzing Short-Term Noise Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation

Simultaneous spike-counts of neural populations are typically modeled by a Gaussian distribution. On short time scales, however, this distribution is too restrictive to describe and analyze multivariate distributions of discrete spike-counts. We present an alternative that is based on copulas and can account for arbitrary marginal distributions, including Poisson and negative binomial distributions as well as second and higher-order interactions. We describe maximum likelihood-based procedures for fitting copula-based models to spike-count data, and we derive a so-called flashlight transformation which makes it possible to move the tail dependence of an arbitrary copula into an arbitrary orthant of the multivariate probability distribution. Mixtures of copulas that combine different dependence structures and thereby model different driving processes simultaneously are also introduced. First, we apply copula-based models to populations of integrate-and-fire neurons receiving partially correlated input and show that the best fitting copulas provide information about the functional connectivity of coupled neurons which can be extracted using the flashlight transformation. We then apply the new method to data which were recorded from macaque prefrontal cortex using a multi-tetrode array. We find that copula-based distributions with negative binomial marginals provide an appropriate stochastic model for the multivariate spike-count distributions rather than the multivariate Poisson latent variables distribution and the often used multivariate normal distribution. The dependence structure of these distributions provides evidence for common inhibitory input to all recorded stimulus encoding neurons. Finally, we show that copula-based models can be successfully used to evaluate neural codes, e. g., to characterize stimulus-dependent spike-count distributions with information measures. This demonstrates that copula-based models are not only a versatile class of models for multivariate distributions of spike-counts, but that those models can be exploited to understand functional dependencies

Central Masses and Broad-Line Region Sizes of Active Galactic Nuclei. II. A Homogeneous Analysis of a Large Reverberation-Mapping Database

We present improved black hole masses for 35 active galactic nuclei (AGNs) based on a complete and consistent reanalysis of broad emission-line reverberation-mapping data. From objects with multiple line measurements, we find that the highest precision measure of the virial product is obtained by using the cross-correlation function centroid (as opposed to the cross-correlation function peak) for the time delay and the line dispersion (as opposed to full width half maximum) for the line width and by measuring the line width in the variable part of the spectrum. Accurate line-width measurement depends critically on avoiding contaminating features, in particular the narrow components of the emission lines. We find that the precision (or random component of the error) of reverberation-based black hole mass measurements is typically around 30%, comparable to the precision attained in measurement of black hole masses in quiescent galaxies by gas or stellar dynamical methods. Based on results presented in a companion paper by Onken et al., we provide a zero-point calibration for the reverberation-based black hole mass scale by using the relationship between black hole mass and host-galaxy bulge velocity dispersion. The scatter around this relationship implies that the typical systematic uncertainties in reverberation-based black hole masses are smaller than a factor of three. We present a preliminary version of a mass-luminosity relationship that is much better defined than any previous attempt. Scatter about the mass-luminosity relationship for these AGNs appears to be real and could be correlated with either Eddington ratio or object inclination.Comment: 61 pages, including 8 Tables and 16 Figures. Accepted for publication in The Astrophysical Journa

Reverberation Mapping Measurements of Black Hole Masses in Six Local Seyfert Galaxies

We present the final results from a high sampling rate, multi-month, spectrophotometric reverberation mapping campaign undertaken to obtain either new or improved Hbeta reverberation lag measurements for several relatively low-luminosity AGNs. We have reliably measured thetime delay between variations in the continuum and Hbeta emission line in six local Seyfert 1 galaxies. These measurements are used to calculate the mass of the supermassive black hole at the center of each of these AGNs. We place our results in context to the most current calibration of the broad-line region (BLR) R-L relationship, where our results remove outliers and reduce the scatter at the low-luminosity end of this relationship. We also present velocity-resolved Hbeta time delay measurements for our complete sample, though the clearest velocity-resolved kinematic signatures have already been published.Comment: 52 pages (AASTeX: 29 pages of text, 8 tables, 7 figures), accepted for publication in the Astrophysical Journa

The magellanic quasars survey. III. Spectroscopic confirmation of 758 active galactic nuclei behind the magellanic clouds

The Magellanic Quasars Survey (MQS) has now increased the number of quasars known behind the Magellanic Clouds by almost an order of magnitude. All survey fields in the Large Magellanic Cloud (LMC) and 70% of those in the Small Magellanic Cloud (SMC) hav

NGC 5548 in a Low-Luminosity State: Implications for the Broad-Line Region

We describe results from a new ground-based monitoring campaign on NGC 5548, the best studied reverberation-mapped AGN. We find that it was in the lowest luminosity state yet recorded during a monitoring program, namely L(5100) = 4.7 x 10^42 ergs s^-1. We determine a rest-frame time lag between flux variations in the continuum and the Hbeta line of 6.3 (+2.6/-2.3) days. Combining our measurements with those of previous campaigns, we determine a weighted black hole mass of M_BH = 6.54 (+0.26/-0.25) x 10^7 M_sun based on all broad emission lines with suitable variability data. We confirm the previously-discovered virial relationship between the time lag of emission lines relative to the continuum and the width of the emission lines in NGC 5548, which is the expected signature of a gravity-dominated broad-line region. Using this lowest luminosity state, we extend the range of the relationship between the luminosity and the time lag in NGC 5548 and measure a slope that is consistent with alpha = 0.5, the naive expectation for the broad line region for an assumed form of r ~ L^alpha. This value is also consistent with the slope recently determined by Bentz et al. for the population of reverberation-mapped AGNs as a whole.Comment: 24 pages, 3 tables, 7 figures, accepted for publication in Ap

The Mass of the Black Hole in the Seyfert 1 Galaxy NGC 4593 from Reverberation Mapping

We present new observations leading to an improved black hole mass estimate for the Seyfert 1 galaxy NGC 4593 as part of a reverberation-mapping campaign conducted at the MDM Observatory. Cross-correlation analysis of the H_beta emission-line light curve with the optical continuum light curve reveals an emission-line time delay of 3.73 (+-0.75) days. By combining this time delay with the H_beta line width, we derive a central black hole mass of M_BH = 9.8(+-2.1)x10^6 M_sun, an improvement in precision of a factor of several over past results.Comment: 22 pages, 3 tables, 5 figures, accepted for publication in Ap

Empty spaces and the value of symbols: Estonia's 'war of monuments' from another angle

Taking as its point of departure the recent heightened discussion surrounding publicly sited monuments in Estonia, this article investigates the issue from the perspective of the country's eastern border city of Narva, focusing especially upon the restoration in 2000 of a 'Swedish Lion' monument to mark the 300th anniversary of Sweden's victory over Russia at the first Battle of Narva. This commemoration is characterised here as a successful local negotiation of a potentially divisive past, as are subsequent commemorations of the Russian conquest of Narva in 1704. A recent proposal to erect a statue of Peter the Great in the city, however, briefly threatened to open a new front in Estonia's ongoing 'war of monuments'. Through a discussion of these episodes, the article seeks to link the Narva case to broader conceptual issues of identity politics, nationalism and post-communist transition

Measuring the mass of the central black hole in the bulgeless galaxy ngc 4395 from gas dynamical modeling

NGC 4395 is a bulgeless spiral galaxy, harboring one of the nearest known type 1 Seyfert nuclei. Although there is no consensus on the mass of its central engine, several estimates suggest it is one of the lightest massive black holes (MBHs) known. We present the first direct dynamical measurement of the mass of this MBH from a combination of two-dimensional gas kinematic data, obtained with the adaptive optics assisted near-infrared integral field spectrograph Gemini/NIFS and high-resolution multiband photometric data from Hubble Space Telescope's Wide Field Camera 3. We use the photometric data to model the shape and stellar mass-to-light ratio of the nuclear star cluster (NSC). From the Gemini/NIFS observations, we derive the kinematics of warm molecular hydrogen gas as traced by emission through the H2 1–0 S(1) transition. These kinematics show a clear rotational signal, with a position angle orthogonal to NGC 4395's radio jet. Our best-fitting tilted ring models of the kinematics of the molecular hydrogen gas contain a black hole with mass M={4}-3+8× {10}5 M⊙ (3σ uncertainties) embedded in an NSC of mass M=2× {10}6 M⊙. Our black hole mass measurement is in excellent agreement with the reverberation mapping mass estimate of Peterson et al. but shows some tension with other mass measurement methods based on accretion signals

Steps Toward Determination of the Size and Structure of the Broad-Line Region in Active Galactic Nuclei. XVI. A Thirteen-Year Study of Spectral Variability in NGC 5548

We present the final installment of an intensive 13-year study of variations of the optical continuum and broad H-beta emission line in the Seyfert 1 galaxy NGC 5548. The data base consists of 1530 optical continuum measurements and 1248 H-beta measurements. The H-beta variations follow the continuum variations closely, with a typical time delay of about 20 days. However, a year-by-year analysis shows that the magnitude of emission-line time delay is correlated with the mean continuum flux. We argue that the data are consistent with the simple model prediction that the size of the broad-line region is proportional to the square root of the ionizing luminosity. Moreover, the apparently linear nature of the correlation between the H-beta response time and the nonstellar optical continuum arises as a consequence of the changing shape of the continuum as it varies, specifically with the optical (5100 A) continuum luminosity proportional to the ultraviolet (1350 A) continuum luminosity to the 0.56 power.Comment: 20 pages plus 4 figures. Accepted for publication in The Astrophysical Journa